FourierParameters

FourierParameters

is an option to Fourier and related functions that specifies the conventions to use in computing Fourier transforms.

Details

  • A typical setting is FourierParameters->{a,b}.
  • Some common choices for {a,b} are {0,1} (default), {-1,1} (data analysis), {1,-1} (signal processing).

Examples

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Basic Examples  (2)

Use a nondefault definition of the discrete Fourier transform:

Use the same definition to get the inverse:

A nondefault definition used for the continuous Fourier transform:

Scope  (3)

A typical pure mathematics or systems-engineering definition of Fourier transform:

Use the same definition for the inverse transform:

A typical data-analysis definition of discrete Fourier transform:

Use the same definition to get the correct inverse:

A common signal-processing definition of Fourier transform:

Discrete Fourier transform:

Discrete-time Fourier transform:

Possible Issues  (2)

The same FourierParameters values need to be used for both forward and inverse transforms:

Here the inverse uses a different choice of FourierParameters:

The second parameter needs to be relatively prime to the data length to guarantee invertibility:

Wolfram Research (1999), FourierParameters, Wolfram Language function, https://reference.wolfram.com/language/ref/FourierParameters.html.

Text

Wolfram Research (1999), FourierParameters, Wolfram Language function, https://reference.wolfram.com/language/ref/FourierParameters.html.

BibTeX

@misc{reference.wolfram_2021_fourierparameters, author="Wolfram Research", title="{FourierParameters}", year="1999", howpublished="\url{https://reference.wolfram.com/language/ref/FourierParameters.html}", note=[Accessed: 24-September-2021 ]}

BibLaTeX

@online{reference.wolfram_2021_fourierparameters, organization={Wolfram Research}, title={FourierParameters}, year={1999}, url={https://reference.wolfram.com/language/ref/FourierParameters.html}, note=[Accessed: 24-September-2021 ]}

CMS

Wolfram Language. 1999. "FourierParameters." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/FourierParameters.html.

APA

Wolfram Language. (1999). FourierParameters. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/FourierParameters.html